Zadeh introduced the concept of fuzzy set to assign to each object encountered in the real physical world that do not have precisely defined criteria of membership a grade of membership ranging between zero and one in 1965 [15]. Kramosil and Micha ?lek defined the concept of fuzzy metric space using continuous t-norms in 1975 [9]. The fuzzy metric spaces have very important applications in quantum physics, particularly, in connections with both string and o?(?) theory which were studied by EI Naschie [14]. Matloka considered bounded and convergent sequences of fuzzy numbers and studied their properties in 1986 [11]. Sequences of fuzzy numbers also were discussed by Nanda [13], Kwon [10], Esi [5] and many others. Burgin introduced the theory of fuzzy limits of functions based on the theory of fuzzy limits of sequences in 2000. He studied and developed the construction of fuzzy limits of functions similar to the one of the fuzzy limits of sequences based on the concept of r?limit of function f [3]. In 2010, Altai defined the fuzzy metric spaces in a new
way,thateveryrealnumberr?Risreplacedbyafuzzynumberr?R, R=Z?Q?Q?,whereifr?Q? or r ? Q\Z will be replaced by a triangular fuzzy number because of density of irrational and rational numbers in R and if r ? Z will be replaced by a singleton fuzzy set because of non density of integer numbers in R [1], and then using the representation theorem (resolution principle) to calculate the arithmetic operations act on ??cuts of fuzzy numbers [4]. And in 2011, Altai defined the limit fuzzy number of the convergent fuzzy sequence in similar way [2]. Our goal is to establish the theory of fuzzy limits of fuzzy functions depending on Altai’s principle, because it is very handy and convenient in the study of the fuzzy arithmeti